American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-5, Issue-5, pp-124-134 www.ajer.org Research Paper
Open Access
Determination of Induction Machine Parameters by Simulation Dr. E.A. Anazia, Engr. Samson Ugochukwu*, Dr. J. C. Onuegbu, Engr. Onyedikachi S.N Department of Electrical Engineering Namdi Azikiwe University Awka, Anambra State, Nigeria
ABSTRACT: A 38.1 Watt fractional horse power induction laboratory test motor model was created using MotorSolve 5.2; an electrical machine design application. Initial machine parameters such as voltage, speed, and main dimensions were selected and fed into the application and simulations ran. The simulated results were presented and analyzed. Unlike other induction machine parameter identification process, this method is simple, flexible and accurate since it does not involve rigorous mathematical manual computations and derivations and can be fine tuned to the best quality by adjusting precision accuracy algorithm embedded in the application. The (FE) finite element block of the machine design application performs all iteration internally and displays the result graphically as well as in discrete form. Keywords: Simulation, Induction Motor, Parameter identification, Finite Element Analysis.
I.
INTRODUCTION
Induction motors are the power horse of industrial revolution and continuous process applications as well as automotive applications; hence various studies had been carried out on their structure, production controls and applications. In recent times the world population had grown beyond imagination despite natural and artificial disasters. These large numbers and the unwitting quest of man to explore the world to its fullest and attain perfection had placed unprecedented demand on design precision. To this effect, technology had continued to place emphasis on design accuracy, a challenge which had led engineers and scientist to develop high precision design applications which are capable of performing large number of mathematical computations within minutes, second or even milliseconds and with lofty accuracy. Finite Element Applications (FEA) are widely used to arrive at high quality design parameters. Finite Element design application which incorporates 3D modeling interface dedicated to induction machine design was used to determine the parameters of the chosen design in this paper as described below. Other FE applications such as, AnsysMultiphysics, COMSOLMultiphysics, ElectNet, according to [1], Flux, SPEED etc can as well be used to perform induction machine parameter identification. It further described the use of Linear Time Harmonics Vector Field Potentials to determine motor parameters. Traditionally, induction motor parameter was determined by three basic laboratory tests on prototype machine according to [2]. These tests; DC Resistance test, Locked Rotor Test, and No Load Test, were time consuming, expensive as prototype machines have to be constructed, and the laboratory equipments necessary to carry out the test and measure all the parameters of interest must be assembled, though the method proved resourceful before the advent of virtual simulators which are now capable of carrying out those task. In finite element systems, the double cage model is found to give a better approximation of the parameters required to design and construct an induction motor fairly accurate [3]. [4] indentified inductions motor parameter using free acceleration and deceleration test results similar to the test described in [2] above. [5] and [6] estimated induction motor parameter by measuring transient stator current alone and applying varying degrees of mathematical optimization algorithms. [7] presented machine parameter identification by means of classical induction motor model used mostly in control applications and involves matrix vector formulation of machine parameters and minimizing them using least square methods. [8] applied modified particle swarm optimization theory to determine induction motor parameters. [9] in his dynamic model of induction motor parameters adopted the same principle of
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classical model to determine motor parameters as was used in [7]. [10] conventionally presented induction motor parameters using manual computations by specifying some initial parameters and working out induction motor parameters using conventional formulae. All these models stated here and various others lists unending, that have been applied to induction motor parameter identification, non is as simple and straight forward as the simulations process described in this article.
II.
MOTOR MODEL
Initial Parameter/ Rating Voltage = 100 Volts Phase = 3∅ Frequency = 50Hz No of Poles = 4 poles Synchronous Speed = 1800 rpm Power Rating = 38.1 or 0.1 HP R1 = Stator Resistance L1 = Stator Inductance R2 = Rotor Resistance L2 = Rotor Inductance A three dimensional as well as x-y view of the motor model is shown below.
Figure 1: 3-D and x-y view of the induction motor model The equivalent circuit model of the motor shown above is illustrated below. R 1, L1, represents stator resistance and inductance respectively. R2 and L2 stands for rotor resistance and inductance. M represents the magnetizing inductance of the machine which may account for eddy current loss and the shunt resistor R c is used to model the core (iron) loss as in the case of standard transformer model [3]. V 0 is the applied 3-phase voltages and I1, Ic, IM, and I2 represents current distribution. S indicates slip as the rotor resistance varies with motor speed.
0
Figure 2: Equivalent circuit model of the induction motor.
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MOTOR EQUATIONS
Input power; đ?‘ƒ = 3đ?‘‰đ??ź cosâ Ąâˆ… đ?‘ƒ = đ?‘‡đ?œ” Where đ?‘‰, đ??ź, cos ∅, đ?‘‡ đ?‘Žđ?‘›đ?‘‘ đ?œ” are voltage, current, power factor, Torque and rotor spindle speed respectively. Impedance; The parallel branch circuit impedance; 1 1 1 1 1 1 = + + +đ?‘— + (3) đ?‘?
đ?‘…đ??ś
đ?‘…2
1−đ?‘ đ?‘…2 đ?‘†
đ?‘€
(1) (2)
đ??ż2
Simplifying gives; đ?‘?= đ?‘?=
1−đ?‘† đ?‘… 2 ∗đ?‘— đ?‘€+đ??ż2 đ?‘† đ?‘†đ?‘… 2 +đ?‘… 2 +đ?‘†đ?‘… 2 đ?‘…đ??ś + +đ?‘— đ?‘€+đ??ż2 đ?‘† đ?‘… đ?‘…đ??ś + đ?‘†2 ∗đ?‘— đ?‘€+đ??ż2 đ?‘… đ?‘…đ??ś + 2 +đ?‘— đ?‘€+đ??ż2 đ?‘† đ?‘… đ?‘…đ??ś + đ?‘†2 ∗đ?‘— đ?‘€+đ??ż2 đ?‘‡ 1 1 đ?‘…2 đ?‘…đ??ś + +đ?‘— đ?‘€+đ??ż2 đ?‘†
đ?‘…đ??ś +đ?‘…2 +
(4) (5)
∴ đ?‘? = đ?‘… + đ?‘—đ??ż +
(6)
Normalizing to remove the complex variable j from the denominator yields, đ?‘…
đ?‘…đ??ś + đ?‘†2 ∗đ?‘— đ?‘€+đ??ż2
đ?‘?đ?‘‡ = đ?‘…1 + đ?‘—đ??ż1 +
đ?‘… đ?‘…đ??ś + đ?‘†2 −đ?‘— đ?‘€+đ??ż2
∗
đ?‘… đ?‘…đ??ś + 2 +đ?‘— đ?‘€+đ??ż2 đ?‘…
đ?‘— đ?‘…đ??ś + 2 đ?‘†
đ?‘?đ?‘‡ = đ?‘…1 + đ?‘—đ??ż1 +
2
�
đ?‘… − đ?‘— 2 đ?‘…đ??ś + 2 đ?‘€+đ??ż2 2 đ?‘†
∗ đ?‘€+đ??ż2
2
đ?‘… đ?‘…đ??ś + 2 đ?‘†
đ?‘… đ?‘…đ??ś + 2 đ?‘†
2
(8)
+ đ?‘€+đ??ż2 2
đ?‘… đ?‘… đ?‘…đ??ś + 2 đ?‘€+đ??ż2 2 + đ?‘— đ?‘…đ??ś + 2 đ?‘† đ?‘†
đ?‘?đ?‘‡ = đ?‘…1 + đ?‘—đ??ż1 +
2
∗ đ?‘€+đ??ż2
(9)
+ đ?‘€+đ??ż2 2
Starting torque in terms of machine parameters; Let đ??¸2 = Rotor e.m.f per phase developed at standstill đ?‘…2 = Rotor resistance per phase đ??ż2 = Rotor inductance per phase at standstill. đ?‘?đ?‘‡đ?‘&#x; = đ?‘…2 2 + đ??ż2 2 = Rotor impedance per phase at standstill. Then; đ??¸2 đ??ź2 = 2 2 đ?‘… 2 +đ??ż 2
cos ∅ =
đ?‘…2 đ?‘?đ?‘‡đ?‘&#x;
=
đ?‘…2
(10) (11)
đ?‘… 2 2 +đ??ż2 2
Therefore starting torque becomes; đ?‘‡đ?‘ đ?‘Ą = đ?‘˜1 đ??¸2 đ??ź2 cos ∅ This implies that; đ?‘‡đ?‘ đ?‘Ą = đ?‘˜1 đ??¸2 ∗
(7)
đ?‘… đ?‘…đ??ś + 2 −đ?‘— đ?‘€+đ??ż2
�
(12)
đ??¸2 đ?‘… 2 2 +đ??ż2 2
∗
đ?‘…2 đ?‘… 2 2 +đ??ż2 2
=
đ?‘˜ 1 đ??¸2 2 đ?‘…2 đ?‘… 2 2 +đ??ż2 2
(13)
But; đ?‘˜1 =
3
(14)
2đ?œ‹đ?‘ đ?‘
where đ?‘ đ?‘ is the synchronous speed. This implies that; đ?‘‡đ?‘ đ?‘Ą =
3 2đ?œ‹đ?‘ đ?‘
∗
đ??¸2 2 đ?‘…2 đ?‘… 2 2 +đ??ż2 2
=
3đ??¸2 2 đ?‘…2 2đ?œ‹đ?‘ đ?‘ đ?‘?đ?‘‡đ?‘&#x; 2
(15)
Dynamic Torque in terms of machine parameters;
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When the machine rotor is on motion, the induced emf and the rotor reactance or inductance is reduced by slip value represented by đ?‘† [11]. Hence dynamic torque or torque under running condition will also be limited by slip as shown in the relation below. đ?‘‡đ??ˇ =
3đ?‘†đ??¸2 2 đ?‘…2
(16)
2đ?œ‹đ?‘ đ?‘ đ?‘†đ?‘?đ?‘‡đ?‘&#x; 2
At standstill, the motor draws double it’s running current before starting known as the starting current and gradually reduces as the motor gathers speed, but is directly proportional to slip since slip action is opposite to that of speed. This is indicated in the relation and figure 5 below; đ?‘† đ??źâˆ? (17) đ?‘ đ?‘
where đ?‘ - slip and đ?‘ đ?‘ synchronous speed. Efficiency and torque relationship to speed and slip is a hyperbolic function stated below.
IV.
MODEL PARAMETER COMPUTATION
With three built in model parameter calculation algorithms; the classical, the conventional and the inductance matrix algorithms, FE automatically computes the crucial parameters of the induction machine as represented in the equivalent circuit diagram redrawn in figure 3 below showing values.
Figure 3: Equivalent circuit model of the induction motor after computation When the model contains rotor bars with skew, inductance matrix method is usually used for parameter computation irrespective of the method selected by the machine designer. This is because it takes into cognizance the magnetizing and leakage inductances, thus producing a more accurate result. The table 1 below shows the parameter values computed to varying degrees of decimal approximation. Figure 4 and table 2 show the name plate data. Table 1: Equivalent circuit data table Values R1 R2 Rc L1 L2 M
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9.901026594 Ί 9.489735585 Ί 10806.40833 Ί 21.17636636 mH 25.2633269 mH 235.0822367 mH
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Figure 4: Name plate data simulated from MotorSolve Table 2: Nameplate data Values Phase Frequency Voltage RPM Current Horsepower Power factor Efficiency
V.
3 60 Hz 100 V 1710 rpm 0.640635467 A 0.050844399 hp 0.477105111 71.61790111 %
SIMULATION RESULTS
Figure 5: Composite plot of Power factor, Voltage, Torque, Efficiency and Current against Rotor speed and Slip in (%). It can be seen from the torque curve above that when slip = 0%, torque also = 0%; hence the curve start from zero. At synchronous or close to synchronous speed, the term sL2 is small compared to R2. Therefore torque is directly proportional to slip(s) and inversely proportional to R2. As slip increases, torque increases as well. If R2 is kept constant, we obtain a straight line relation seen between zero and about 20% slip in figure 5 above. Increase in torque continues as slip increases (more motor load), until maximum torque, pull-out or breakdown is reached at about 44-55% slip. Any increase in motor load or slip beyond this point slows down the motor thereby reducing the torque developed by the motor. The power factor curve shows that the motor has a power factor of 0.7-0.8 with maximum power factor achieved at synchronous speed or near synchronism. The efficiency of the motor increases as the motor accelerates and become maximum at synchronous speed as shown in figure 5 above. With the presence of drive circuit, the voltage used by the motor for its operation is constant as shown but the current wave form indicates high current at starting which is an indication that the motor resultant reactance is low at this stage but increases as the motor speed and temperature increases. It is also very clear that induction motor draws double the current required to run it normally during start up.
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S/N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Rotor speed (rpm) 1800 1782 1764 1746 1728 1710 1692 1674 1656 1638 1620 1602 1584 1566 1548 1530 1512 1494 1476 1458
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
1440 1422 1404 1386 1368 1350 1332 1314 1296 1278 1260 1242 1224 1206 1188 1170 1152 1134 1116 1098 1080 1062 1044 1026
Table 3: Data used to plot composite characteristic of figure 5 RMS Rotor Voltage RMS slip (%) Torque (N·m) Efficiency (%) (V) current (A) 0 0 0 100 0.593999144 1 0.045659935 42.74063487 100 0.592457956 2 0.089677061 58.38708377 100 0.596857009 3 0.132032725 65.79050517 100 0.606748708 4 0.172717425 69.62868573 100 0.621556859 5 0.211730067 71.61790111 100 0.640635467 6 0.249077212 72.53566323 100 0.663323191 7 0.284772315 72.784883 100 0.688985148 8 0.31883498 72.59486396 100 0.7170396 9 0.351290228 72.10544502 100 0.746971249 10 0.382167796 71.40654511 100 0.778334676 11 0.411501465 70.55844837 100 0.810751554 12 0.439328437 69.60295065 100 0.84390453 13 0.465688742 68.56983456 100 0.877529767 14 0.490624692 67.48080747 100 0.911409354 15 0.514180389 66.35199073 100 0.945364223 16 0.536401265 65.19554565 100 0.979247856 17 0.557333671 64.02076618 100 1.012940872 18 0.577024517 62.83483157 100 1.046346444 19 0.595520938 61.64333613 100 1.079386468 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
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0.612870013 0.62911851 0.644312675 0.658498042 0.671719282 0.684020071 0.695442983 0.706029408 0.715819485 0.724852054 0.733164623 0.740793343 0.747773004 0.754137033 0.759917499 0.765145134 0.76984935 0.774058268 0.777798748 0.781096418 0.783975716 0.786459924 0.788571207 0.790330655
60.45066936 59.2602934 58.0749487 56.89680847 55.72759628 54.56867648 53.42112449 52.28578195 51.16330034 50.05417582 48.95877711 47.87736813 46.81012633 45.75715771 44.71850917 43.69417869 42.68412376 41.6882684 40.70650904 39.73871941 38.78475468 37.8444549 36.91764798 36.00415207
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
1.111998384 1.144132539 1.175750015 1.206820826 1.237322425 1.267238471 1.296557796 1.325273544 1.353382459 1.380884279 1.407781226 1.434077584 1.459779338 1.484893864 1.509429674 1.533396196 1.556803585 1.579662567 1.601984301 1.623780268 1.645062169 1.665841846 1.686131207 1.705942174
2016
Power factor 0.110797571 0.194273015 0.274448497 0.349157791 0.41694505 0.477105111 0.529572686 0.57473833 0.613260862 0.645915952 0.673492389 0.696730907 0.716294332 0.732757932 0.746611365 0.758266397 0.76806685 0.776298787 0.78319996 0.788968105 0.793767997 0.797737331 0.80099157 0.803627901 0.805728468 0.807362986 0.80859088 0.809463016 0.810023117 0.810308918 0.810353115 0.810184147 0.809826838 0.809302933 0.80863154 0.807829504 0.806911721 0.805891391 0.80478025 0.803588752 0.802326233 0.801001045 0.799620674 0.798191843
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45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
1008 990 972 954 936 918 900 882 864 846 828 810 792 774 756 738 720 702 684 666 648
44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
0.79175832 0.79287326 0.793693577 0.794236457 0.79451821 0.794554308 0.794359423 0.793947465 0.793331615 0.79252436 0.791537528 0.790382318 0.789069335 0.787608613 0.786009648 0.784281427 0.782432447 0.780470748 0.778403931 0.776239183 0.773983299
35.10377776 34.21632976 33.34160846 32.47941117 31.62953322 30.79176885 29.96591203 29.15175705 28.34909913 27.55773486 26.77746258 26.00808274 25.24939812 24.50121411 23.76333884 23.03558336 22.31776173 21.60969114 20.91119193 20.22208771 19.54220531
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
1.725286625 1.744176357 1.76262305 1.780638236 1.798233276 1.815419342 1.832207398 1.84860819 1.864632234 1.880289811 1.895590961 1.910545479 1.925162912 1.939452562 1.953423483 1.967084484 1.980444132 1.993510752 2.006292434 2.018797036 2.031032185
0.7967206 0.795212391 0.793672128 0.792104246 0.790512755 0.788901283 0.787273112 0.785631221 0.783978305 0.782316812 0.780648963 0.778976771 0.777302065 0.775626504 0.773951593 0.772278697 0.770609054 0.768943785 0.767283907 0.765630336 0.763983904
66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
630 612 594 576 558 540 522 504 486 468 450 432 414 396 378 360 342 324 306 288 270 252 234 216
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88
0.771642701 0.769223458 0.766731306 0.764171664 0.761549652 0.758870105 0.756137591 0.753356421 0.750530668 0.747664176 0.744760574 0.741823287 0.738855544 0.735860396 0.732840718 0.729799221 0.726738462 0.723660854 0.720568666 0.717464041 0.714348994 0.711225425 0.708095123 0.704959769
18.87137484 18.20942971 17.55620656 16.91154533 16.27528915 15.64728439 15.02738057 14.41543033 13.8112894 13.21481657 12.62587358 12.04432516 11.47003886 10.90288513 10.34273716 9.789470857 9.242964818 8.703100241 8.169760881 7.642832992 7.122205277 6.60776883 6.099417082 5.59704575
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
2.043005288 2.05472353 2.066193884 2.077423113 2.088417778 2.09918424 2.109728671 2.12005705 2.130175178 2.140088678 2.149803 2.159323429 2.168655088 2.177802942 2.186771806 2.195566346 2.204191089 2.21265042 2.220948593 2.229089733 2.237077837 2.244916784 2.252610335 2.260162139
0.762345359 0.760715375 0.759094558 0.757483454 0.755882549 0.754292278 0.752713028 0.751145141 0.749588918 0.748044626 0.746512495 0.744992724 0.743485484 0.741990918 0.740509148 0.73904027 0.737584361 0.736141481 0.73471167 0.733294954 0.731891343 0.730500836 0.729123418 0.727759064
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American Journal of Engineering Research (AJER) 90 91 92 93 94 95 96 97 98 99 100 101
198 180 162 144 126 108 90 72 54 36 18 0
89 90 91 92 93 94 95 96 97 98 99 100
0.701820949 0.69868015 0.695538773 0.692398135 0.689259471 0.686123943 0.68299264 0.679866583 0.676746731 0.673633981 0.670529173 0.667433094
VI.
5.100552783 4.609838311 4.124804593 3.645355972 3.171398817 2.702841486 2.23959427 1.781569353 1.328680762 0.880844328 0.437977639 0
100 100 100 100 100 100 100 100 100 100 100 100
2.267575732 2.274854547 2.282001915 2.289021065 2.295915133 2.30268716 2.309340099 2.315876816 2.322300092 2.328612629 2.334817049 2.340915897
2016 0.726407738 0.725069395 0.723743984 0.722431442 0.721131702 0.71984469 0.718570327 0.717308528 0.716059203 0.714822259 0.713597598 0.712385121
HEAT CAPACITY MODEL
Every matter has a certain amount of heat it can withstand over a given period of time before changing state; known as the heat capacity. If the temperature of the body is not exceeded far beyond acceptable limit within the operating time, the heat capacity of the body remains constant. Let ∠= heat capacity in Joules per Kg per 0C đ?œƒ = Maximum temperature the body can withstand in time t. đ?‘Ą = Operating time The heat capacity can be related to the temperature and operating time as follows; ∠âˆ? đ?œƒđ?‘Ą; ⇒ ∠= â„Žđ?œƒđ?‘Ą (20) where â„Ž is a constant of proportionality known as specific heat capacity. A plot of ∠against time đ?‘Ą figure 6 below, show constant range of values provided maximum permissible temperature and operating time are not exceeded beyond acceptable limit for each individual motor part.
Figure 6: Composite plot of motor material Heat Capacity against operation time.
VII.
THERMAL MODEL OF THE MOTOR
A simple thermal model, assuming a homogeneous body of motor can be obtained as follows [12]: At time‘t’, let the motor has following parameters Q1 = Heat developed, Joules/sec or watts, Q2 = Heat dissipated to the cooling medium, watts, W = Weight of the active parts of the machine. h = Specific heat, Joules per Kg per 0C. S = Cooling Surface, m2 d = Co-efficient of heat transfer, Joules/Sec/m2/0C θ = Mean temperature rise oC
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At time dt, let the temperature rise of the machine be dθ, Therefore, heat absorbed by the machine = (Heat generated inside the machine – Heat dissipated to the surrounding) Where, đ?‘‘đ?œƒ = đ?‘„1 − đ?‘„2 đ?‘‘đ?‘Ą (21) Since, đ?‘„2 = đ?œƒđ?‘‘đ?‘† (22) Substituting (ii) into (i), gives đ?‘‘đ?œƒ đ??ś = đ?‘„1 − đ??ˇđ?œƒ (23) đ?‘‘đ?‘Ą Where ∠= â„Žđ?‘Š and đ??ˇ = đ?‘‘đ?‘†. ∠is the thermal heat capacity of the machine in watts/oC and đ??ˇ is the heat dissipation constant in watts/oC. The first order differential equation of the equation – above is stated below đ?‘Ą đ?œƒ = ∄đ?‘ đ?‘ + đ??žđ?‘’ − đ?œ? (24) đ?‘„ Where ∄đ?‘ đ?‘ = 1 đ??ˇ đ?‘Žđ?‘›đ?‘‘ đ?œ? = ∠đ??ˇ (25) To solve for K we put t = 0 in equation (iii) and the solution becomes đ?‘Ą đ?‘Ą đ?œƒ = ∄đ?‘ đ?‘ 1 − đ??žđ?‘’ − đ?œ? + đ?œƒ1 đ?‘’ − đ?œ? (26) Represented in the graph of figure 7 is the graph of temperature characteristics of selected machine parts which are based on the relation of equation (23) above. Table 4: Data used to plot composite heat capacity of figure 6
Table 5: Data used to plot composite temperature characteristics of figure 7
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Figure 7: Plot of Temperature variation of selected motor parts against time
VIII. CONCLUSION Various authors had written on induction motor parameter identification process and model, majority of which are highly complex and time consuming but this paper presented a model based on simulation using finite element analysis application. (FEA). The method is highly efficient in terms of time and value precision utilizing direct and easily discernible mathematical models to plot performance characteristics graphs. It is highly flexible as it offers means for model initial parameter variation and consequent re-calculation of required motor parameter with just click of a button. This method is suitable for laboratory experiments and tutorials with an insight into industrial experiments with moderate improvement in design. REFERENCES [1].
[2]. [3]. [4]. [5].
[6].
[7]. [8]. [9]. [10].
[11]. [12].
Mayukh Bose, Anshuman Bhatacharjee, & Sudha R. (2012), Calculation of Induction Motor Model Parameters Using Finite Element Method. International Journal of Soft Computing and Engineering (ISCE), Vol. 2(3), July 2012. Andy Knight. Determination of Induction Machine Parameters, Schulich School of Engineering Retrieved from: http://people.ucalgary.ca/%7/Eaknigh. Wikipedia, Induction Motor Model. Retrieved from: http://www.openelectrical.org/wiki/index.php?title=Induction_Motor_Model Marin Despalatovic, Martin Jadric, Bozo Terzic (2005), Identification of Induction Motor Parameters from Free Acceleration and Deceleration Tests. AUTOMATIKA Vol 46(3-4). Christopher Laughman, Steven B. Leeb, Leslie K. Norford, Steven R. Shaw§ & Peter R. Armstrong, (2016), A two-step method for estimating the parameters of induction machine models. Energy Conversion Congress and Exposition, 2009. ECCE 2009. IEEE. 2009. 262-269. © 2009 Institute of Electrical and Electronics Engineers. DOI: http://dx.doi.org/10.1109/ECCE.2009.5316204. Steven R. Shaw, & Steven B. Leeb, (1999), Identification of Induction Motor Parameters from Transient Stator Current Measurements. IEEE Transactions on Industrial Electronics, Vol. 46, NO. 1, FEBRUARY 1999. Ali Keyhani, Wenzhe Lu, & Bogdan Proca Modeling and Parameter Identification of Electric Machines, Ohio State University, Columbus, Ohio. Hassan M. Emara, Wesam Elshamy & A. Bahgat (), Parameter Identification of Induction Motor Using Modified Particle Swarm Optimization Algorithm. Journal. B. Robyns et al (2012). Vector Control of Induction Machines, Journal of Power Systems, DOI: 10.1007/978-0-85729-901-7_2, Springer-Verlag London 2012. I. Daut, K. Anayet, M. Irwanto, N. Gomesh, M. Muzhar, & M. Asri, Syatirah, (2009) Parameters Calculation of 5 HP AC Induction Motor Proceedings of International Conference on Applications and Design in Mechanical Engineering (ICADME) 11 – 13 October 2009, Batu Ferringhi, Penang, MALAYSIA. B.L Theraja, A.K Theraja. (2005). A text book of Electrical Technology, Volume I, S. Chand and Company Ram Nagar, New Delhi PalmSens, The parallel RL Circuit. Retrieved from: http://www.electrical4u.com/rl-parallel-circuit/#
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Authors Dr. Anazia E. A., Department of Electrical Engineering, Nnamdi Azikiwe University Awka, Anambra State, Nigeria. Dr. Anazia is a lecturer at the above mentioned University. He is a researcher and a senior consulting Engineer. Email: aninyemunzele@yahoo.com
Engr. Samson Ugochukwu E., M.Eng. Student, Nnamdi Azikiwe University Awka, Anambra State, Nigeria., Administrator Madonna University Web based Portal, and IT Support Officer Madonna University Nigeria, Email: samson.uedeh@ymail.com,
Dr. OnuegbuJ. C., Department of Electrical Engineering Nnamdi Azikiwe University Awka, Anambra State, Nigeria.Dr. Onuegbu is a researcher and a lecturer in the above mentioned Institution. Areas of research interest are Machines, high Voltage Engineering and renewable energy. Email: jc.onuegbu@unizik.edu.ng
www.ajer.org
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